Hangartner's Convergence Diagnostic
Hangartner et al. (2011) proposed a convergence diagnostic for discrete Markov chains. A simple Pearson's Chi-squared test for two or more non-overlapping periods of a discrete Markov chain is a reliable diagnostic of convergence. It does not rely upon the estimation of spectral density, on suspect normality assumptions, or determining overdispersion within a small number of outcomes, all of which can be problematic with discrete measures. A discrete Markov chain is split into two or more non-overlapping windows. Two windows are recommended, and results may be sensitive to the number of selected windows, as well as sample size. As such, a user may try several window configurations before concluding there is no evidence of non-convergence.
As the number of discrete events in the sample space increases, this diagnostic becomes less appropriate and standard diagnostics become more appropriate.
Hangartner.Diagnostic(x, J=2)
x |
This required argument is a vector of marginal posterior
samples of a discrete Markov chain, such as selected from the output
of |
J |
This argument specifies the number J of windows to be used, and defaults to J=2. |
The Hangartner.Diagnostic returns an object of class
hangartner, including the output from a Pearson's Chi-squared
test. A frequentist p-value less than or equal to 0.05 is usually
considered to be indicative of non-convergence.
Statisticat, LLC. software@bayesian-inference.com
Hangartner, D., Gill, J., and Cranmer, S., (2011). "An MCMC Diagnostic for Purely Discrete Parameters". Paper presented at the annual meeting of the Southern Political Science Association, Hotel InterContinental, New Orleans, Louisiana Online.
library(LaplacesDemon) N <- 1000 K <- 3 x <- rcat(N, rep(1/K,K)) hd <- Hangartner.Diagnostic(x, J=2) hd
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